My preceding paper on this topic (Otaki ) explored whether the equilibrium existence proof in Lucas  is truly complete. We showed that the proof is incomplete that some additional conditions are required to complete the job. In this paper, we explore another ambiguity in Lucas’s model, which has been pointed out by Grammond (see Lucas ): can the model transform the joint probability density function of the exogenous environment into one that which includes market equilibrium information? This problem is peculiar to the signal extraction problem compatible with the market equilibrium condition. The result indicates that although Lucas  was fundamentally correct in refuting Grammond’s critique, the model contains another crucial assumption concerning the property of the equilibrium function, namely, one-to-one correspondence from the environmental variable to the equilibrium price, which has not been proved by Lucas  to date.